xref: /libCEED/backends/ref/ceed-ref-operator.c (revision d36c159f42e9222d4587decadab914cf55859f56) 
1 // Copyright (c) 2017-2018, Lawrence Livermore National Security, LLC.
2 // Produced at the Lawrence Livermore National Laboratory. LLNL-CODE-734707.
3 // All Rights reserved. See files LICENSE and NOTICE for details.
4 //
5 // This file is part of CEED, a collection of benchmarks, miniapps, software
6 // libraries and APIs for efficient high-order finite element and spectral
7 // element discretizations for exascale applications. For more information and
8 // source code availability see http://github.com/ceed.
9 //
10 // The CEED research is supported by the Exascale Computing Project 17-SC-20-SC,
11 // a collaborative effort of two U.S. Department of Energy organizations (Office
12 // of Science and the National Nuclear Security Administration) responsible for
13 // the planning and preparation of a capable exascale ecosystem, including
14 // software, applications, hardware, advanced system engineering and early
15 // testbed platforms, in support of the nation's exascale computing imperative.
16 
17 #include "ceed-ref.h"
18 
19 //------------------------------------------------------------------------------
20 // Setup Input/Output Fields
21 //------------------------------------------------------------------------------
22 static int CeedOperatorSetupFields_Ref(CeedQFunction qf, CeedOperator op,
23                                        bool inOrOut,
24                                        CeedVector *fullevecs, CeedVector *evecs,
25                                        CeedVector *qvecs, CeedInt starte,
26                                        CeedInt numfields, CeedInt Q) {
27   CeedInt dim, ierr, size, P;
28   Ceed ceed;
29   ierr = CeedOperatorGetCeed(op, &ceed); CeedChk(ierr);
30   CeedBasis basis;
31   CeedElemRestriction Erestrict;
32   CeedOperatorField *opfields;
33   CeedQFunctionField *qffields;
34   if (inOrOut) {
35     ierr = CeedOperatorGetFields(op, NULL, &opfields); CeedChk(ierr);
36     ierr = CeedQFunctionGetFields(qf, NULL, &qffields); CeedChk(ierr);
37   } else {
38     ierr = CeedOperatorGetFields(op, &opfields, NULL); CeedChk(ierr);
39     ierr = CeedQFunctionGetFields(qf, &qffields, NULL); CeedChk(ierr);
40   }
41 
42   // Loop over fields
43   for (CeedInt i=0; i<numfields; i++) {
44     CeedEvalMode emode;
45     ierr = CeedQFunctionFieldGetEvalMode(qffields[i], &emode); CeedChk(ierr);
46 
47     if (emode != CEED_EVAL_WEIGHT) {
48       ierr = CeedOperatorFieldGetElemRestriction(opfields[i], &Erestrict);
49       CeedChk(ierr);
50       ierr = CeedElemRestrictionCreateVector(Erestrict, NULL,
51                                              &fullevecs[i+starte]);
52       CeedChk(ierr);
53     }
54 
55     switch(emode) {
56     case CEED_EVAL_NONE:
57       ierr = CeedQFunctionFieldGetSize(qffields[i], &size); CeedChk(ierr);
58       ierr = CeedVectorCreate(ceed, Q*size, &qvecs[i]); CeedChk(ierr);
59       break;
60     case CEED_EVAL_INTERP:
61       ierr = CeedQFunctionFieldGetSize(qffields[i], &size); CeedChk(ierr);
62       ierr = CeedElemRestrictionGetElementSize(Erestrict, &P);
63       CeedChk(ierr);
64       ierr = CeedVectorCreate(ceed, P*size, &evecs[i]); CeedChk(ierr);
65       ierr = CeedVectorCreate(ceed, Q*size, &qvecs[i]); CeedChk(ierr);
66       break;
67     case CEED_EVAL_GRAD:
68       ierr = CeedOperatorFieldGetBasis(opfields[i], &basis); CeedChk(ierr);
69       ierr = CeedQFunctionFieldGetSize(qffields[i], &size); CeedChk(ierr);
70       ierr = CeedBasisGetDimension(basis, &dim); CeedChk(ierr);
71       ierr = CeedElemRestrictionGetElementSize(Erestrict, &P);
72       CeedChk(ierr);
73       ierr = CeedVectorCreate(ceed, P*size/dim, &evecs[i]); CeedChk(ierr);
74       ierr = CeedVectorCreate(ceed, Q*size, &qvecs[i]); CeedChk(ierr);
75       break;
76     case CEED_EVAL_WEIGHT: // Only on input fields
77       ierr = CeedOperatorFieldGetBasis(opfields[i], &basis); CeedChk(ierr);
78       ierr = CeedVectorCreate(ceed, Q, &qvecs[i]); CeedChk(ierr);
79       ierr = CeedBasisApply(basis, 1, CEED_NOTRANSPOSE, CEED_EVAL_WEIGHT,
80                             CEED_VECTOR_NONE, qvecs[i]); CeedChk(ierr);
81       break;
82     case CEED_EVAL_DIV:
83       break; // Not implemented
84     case CEED_EVAL_CURL:
85       break; // Not implemented
86     }
87   }
88   return 0;
89 }
90 
91 //------------------------------------------------------------------------------
92 // Setup Operator
93 //------------------------------------------------------------------------------/*
94 static int CeedOperatorSetup_Ref(CeedOperator op) {
95   int ierr;
96   bool setupdone;
97   ierr = CeedOperatorGetSetupStatus(op, &setupdone); CeedChk(ierr);
98   if (setupdone) return 0;
99   Ceed ceed;
100   ierr = CeedOperatorGetCeed(op, &ceed); CeedChk(ierr);
101   CeedOperator_Ref *impl;
102   ierr = CeedOperatorGetData(op, (void *)&impl); CeedChk(ierr);
103   CeedQFunction qf;
104   ierr = CeedOperatorGetQFunction(op, &qf); CeedChk(ierr);
105   CeedInt Q, numinputfields, numoutputfields;
106   ierr = CeedOperatorGetNumQuadraturePoints(op, &Q); CeedChk(ierr);
107   ierr = CeedQFunctionGetIdentityStatus(qf, &impl->identityqf); CeedChk(ierr);
108   ierr = CeedQFunctionGetNumArgs(qf, &numinputfields, &numoutputfields);
109   CeedChk(ierr);
110   CeedOperatorField *opinputfields, *opoutputfields;
111   ierr = CeedOperatorGetFields(op, &opinputfields, &opoutputfields);
112   CeedChk(ierr);
113   CeedQFunctionField *qfinputfields, *qfoutputfields;
114   ierr = CeedQFunctionGetFields(qf, &qfinputfields, &qfoutputfields);
115   CeedChk(ierr);
116 
117   // Allocate
118   ierr = CeedCalloc(numinputfields + numoutputfields, &impl->evecs);
119   CeedChk(ierr);
120   ierr = CeedCalloc(numinputfields + numoutputfields, &impl->edata);
121   CeedChk(ierr);
122 
123   ierr = CeedCalloc(16, &impl->inputstate); CeedChk(ierr);
124   ierr = CeedCalloc(16, &impl->evecsin); CeedChk(ierr);
125   ierr = CeedCalloc(16, &impl->evecsout); CeedChk(ierr);
126   ierr = CeedCalloc(16, &impl->qvecsin); CeedChk(ierr);
127   ierr = CeedCalloc(16, &impl->qvecsout); CeedChk(ierr);
128 
129   impl->numein = numinputfields; impl->numeout = numoutputfields;
130 
131   // Set up infield and outfield evecs and qvecs
132   // Infields
133   ierr = CeedOperatorSetupFields_Ref(qf, op, 0, impl->evecs,
134                                      impl->evecsin, impl->qvecsin, 0,
135                                      numinputfields, Q);
136   CeedChk(ierr);
137   // Outfields
138   ierr = CeedOperatorSetupFields_Ref(qf, op, 1, impl->evecs,
139                                      impl->evecsout, impl->qvecsout,
140                                      numinputfields, numoutputfields, Q);
141   CeedChk(ierr);
142 
143   // Identity QFunctions
144   if (impl->identityqf) {
145     CeedEvalMode inmode, outmode;
146     CeedQFunctionField *infields, *outfields;
147     ierr = CeedQFunctionGetFields(qf, &infields, &outfields); CeedChk(ierr);
148 
149     for (CeedInt i=0; i<numinputfields; i++) {
150       ierr = CeedQFunctionFieldGetEvalMode(infields[i], &inmode);
151       CeedChk(ierr);
152       ierr = CeedQFunctionFieldGetEvalMode(outfields[i], &outmode);
153       CeedChk(ierr);
154 
155       ierr = CeedVectorDestroy(&impl->qvecsout[i]); CeedChk(ierr);
156       impl->qvecsout[i] = impl->qvecsin[i];
157       ierr = CeedVectorAddReference(impl->qvecsin[i]); CeedChk(ierr);
158     }
159   }
160 
161   ierr = CeedOperatorSetSetupDone(op); CeedChk(ierr);
162 
163   return 0;
164 }
165 
166 //------------------------------------------------------------------------------
167 // Setup Operator Inputs
168 //------------------------------------------------------------------------------
169 static inline int CeedOperatorSetupInputs_Ref(CeedInt numinputfields,
170     CeedQFunctionField *qfinputfields, CeedOperatorField *opinputfields,
171     CeedVector invec, const bool skipactive, CeedOperator_Ref *impl,
172     CeedRequest *request) {
173   CeedInt ierr;
174   CeedEvalMode emode;
175   CeedVector vec;
176   CeedElemRestriction Erestrict;
177   uint64_t state;
178 
179   for (CeedInt i=0; i<numinputfields; i++) {
180     // Get input vector
181     ierr = CeedOperatorFieldGetVector(opinputfields[i], &vec); CeedChk(ierr);
182     if (vec == CEED_VECTOR_ACTIVE) {
183       if (skipactive)
184         continue;
185       else
186         vec = invec;
187     }
188 
189     ierr = CeedQFunctionFieldGetEvalMode(qfinputfields[i], &emode);
190     CeedChk(ierr);
191     // Restrict and Evec
192     if (emode == CEED_EVAL_WEIGHT) { // Skip
193     } else {
194       // Restrict
195       ierr = CeedVectorGetState(vec, &state); CeedChk(ierr);
196       // Skip restriction if input is unchanged
197       if (state != impl->inputstate[i] || vec == invec) {
198         ierr = CeedOperatorFieldGetElemRestriction(opinputfields[i], &Erestrict);
199         CeedChk(ierr);
200         ierr = CeedElemRestrictionApply(Erestrict, CEED_NOTRANSPOSE, vec,
201                                         impl->evecs[i], request); CeedChk(ierr);
202         impl->inputstate[i] = state;
203       }
204       // Get evec
205       ierr = CeedVectorGetArrayRead(impl->evecs[i], CEED_MEM_HOST,
206                                     (const CeedScalar **) &impl->edata[i]);
207       CeedChk(ierr);
208     }
209   }
210   return 0;
211 }
212 
213 //------------------------------------------------------------------------------
214 // Input Basis Action
215 //------------------------------------------------------------------------------
216 static inline int CeedOperatorInputBasis_Ref(CeedInt e, CeedInt Q,
217     CeedQFunctionField *qfinputfields, CeedOperatorField *opinputfields,
218     CeedInt numinputfields, const bool skipactive, CeedOperator_Ref *impl) {
219   CeedInt ierr;
220   CeedInt dim, elemsize, size;
221   CeedElemRestriction Erestrict;
222   CeedEvalMode emode;
223   CeedBasis basis;
224 
225   for (CeedInt i=0; i<numinputfields; i++) {
226     // Skip active input
227     if (skipactive) {
228       CeedVector vec;
229       ierr = CeedOperatorFieldGetVector(opinputfields[i], &vec); CeedChk(ierr);
230       if (vec == CEED_VECTOR_ACTIVE)
231         continue;
232     }
233     // Get elemsize, emode, size
234     ierr = CeedOperatorFieldGetElemRestriction(opinputfields[i], &Erestrict);
235     CeedChk(ierr);
236     ierr = CeedElemRestrictionGetElementSize(Erestrict, &elemsize);
237     CeedChk(ierr);
238     ierr = CeedQFunctionFieldGetEvalMode(qfinputfields[i], &emode);
239     CeedChk(ierr);
240     ierr = CeedQFunctionFieldGetSize(qfinputfields[i], &size); CeedChk(ierr);
241     // Basis action
242     switch(emode) {
243     case CEED_EVAL_NONE:
244       ierr = CeedVectorSetArray(impl->qvecsin[i], CEED_MEM_HOST,
245                                 CEED_USE_POINTER,
246                                 &impl->edata[i][e*Q*size]); CeedChk(ierr);
247       break;
248     case CEED_EVAL_INTERP:
249       ierr = CeedOperatorFieldGetBasis(opinputfields[i], &basis); CeedChk(ierr);
250       ierr = CeedVectorSetArray(impl->evecsin[i], CEED_MEM_HOST,
251                                 CEED_USE_POINTER,
252                                 &impl->edata[i][e*elemsize*size]);
253       CeedChk(ierr);
254       ierr = CeedBasisApply(basis, 1, CEED_NOTRANSPOSE,
255                             CEED_EVAL_INTERP, impl->evecsin[i],
256                             impl->qvecsin[i]); CeedChk(ierr);
257       break;
258     case CEED_EVAL_GRAD:
259       ierr = CeedOperatorFieldGetBasis(opinputfields[i], &basis); CeedChk(ierr);
260       ierr = CeedBasisGetDimension(basis, &dim); CeedChk(ierr);
261       ierr = CeedVectorSetArray(impl->evecsin[i], CEED_MEM_HOST,
262                                 CEED_USE_POINTER,
263                                 &impl->edata[i][e*elemsize*size/dim]);
264       CeedChk(ierr);
265       ierr = CeedBasisApply(basis, 1, CEED_NOTRANSPOSE,
266                             CEED_EVAL_GRAD, impl->evecsin[i],
267                             impl->qvecsin[i]); CeedChk(ierr);
268       break;
269     case CEED_EVAL_WEIGHT:
270       break;  // No action
271     // LCOV_EXCL_START
272     case CEED_EVAL_DIV:
273     case CEED_EVAL_CURL: {
274       ierr = CeedOperatorFieldGetBasis(opinputfields[i], &basis);
275       CeedChk(ierr);
276       Ceed ceed;
277       ierr = CeedBasisGetCeed(basis, &ceed); CeedChk(ierr);
278       return CeedError(ceed, 1, "Ceed evaluation mode not implemented");
279       // LCOV_EXCL_STOP
280     }
281     }
282   }
283   return 0;
284 }
285 
286 //------------------------------------------------------------------------------
287 // Output Basis Action
288 //------------------------------------------------------------------------------
289 static inline int CeedOperatorOutputBasis_Ref(CeedInt e, CeedInt Q,
290     CeedQFunctionField *qfoutputfields, CeedOperatorField *opoutputfields,
291     CeedInt numinputfields, CeedInt numoutputfields, CeedOperator op,
292     CeedOperator_Ref *impl) {
293   CeedInt ierr;
294   CeedInt dim, elemsize, size;
295   CeedElemRestriction Erestrict;
296   CeedEvalMode emode;
297   CeedBasis basis;
298 
299   for (CeedInt i=0; i<numoutputfields; i++) {
300     // Get elemsize, emode, size
301     ierr = CeedOperatorFieldGetElemRestriction(opoutputfields[i], &Erestrict);
302     CeedChk(ierr);
303     ierr = CeedElemRestrictionGetElementSize(Erestrict, &elemsize);
304     CeedChk(ierr);
305     ierr = CeedQFunctionFieldGetEvalMode(qfoutputfields[i], &emode);
306     CeedChk(ierr);
307     ierr = CeedQFunctionFieldGetSize(qfoutputfields[i], &size); CeedChk(ierr);
308     // Basis action
309     switch(emode) {
310     case CEED_EVAL_NONE:
311       break; // No action
312     case CEED_EVAL_INTERP:
313       ierr = CeedOperatorFieldGetBasis(opoutputfields[i], &basis);
314       CeedChk(ierr);
315       ierr = CeedVectorSetArray(impl->evecsout[i], CEED_MEM_HOST,
316                                 CEED_USE_POINTER,
317                                 &impl->edata[i + numinputfields][e*elemsize*size]);
318       CeedChk(ierr);
319       ierr = CeedBasisApply(basis, 1, CEED_TRANSPOSE,
320                             CEED_EVAL_INTERP, impl->qvecsout[i],
321                             impl->evecsout[i]); CeedChk(ierr);
322       break;
323     case CEED_EVAL_GRAD:
324       ierr = CeedOperatorFieldGetBasis(opoutputfields[i], &basis);
325       CeedChk(ierr);
326       ierr = CeedBasisGetDimension(basis, &dim); CeedChk(ierr);
327       ierr = CeedVectorSetArray(impl->evecsout[i], CEED_MEM_HOST,
328                                 CEED_USE_POINTER,
329                                 &impl->edata[i + numinputfields][e*elemsize*size/dim]);
330       CeedChk(ierr);
331       ierr = CeedBasisApply(basis, 1, CEED_TRANSPOSE,
332                             CEED_EVAL_GRAD, impl->qvecsout[i],
333                             impl->evecsout[i]); CeedChk(ierr);
334       break;
335     // LCOV_EXCL_START
336     case CEED_EVAL_WEIGHT: {
337       Ceed ceed;
338       ierr = CeedOperatorGetCeed(op, &ceed); CeedChk(ierr);
339       return CeedError(ceed, 1, "CEED_EVAL_WEIGHT cannot be an output "
340                        "evaluation mode");
341     }
342     case CEED_EVAL_DIV:
343     case CEED_EVAL_CURL: {
344       Ceed ceed;
345       ierr = CeedOperatorGetCeed(op, &ceed); CeedChk(ierr);
346       return CeedError(ceed, 1, "Ceed evaluation mode not implemented");
347       // LCOV_EXCL_STOP
348     }
349     }
350   }
351   return 0;
352 }
353 
354 //------------------------------------------------------------------------------
355 // Restore Input Vectors
356 //------------------------------------------------------------------------------
357 static inline int CeedOperatorRestoreInputs_Ref(CeedInt numinputfields,
358     CeedQFunctionField *qfinputfields, CeedOperatorField *opinputfields,
359     const bool skipactive, CeedOperator_Ref *impl) {
360   CeedInt ierr;
361   CeedEvalMode emode;
362 
363   for (CeedInt i=0; i<numinputfields; i++) {
364     // Skip active inputs
365     if (skipactive) {
366       CeedVector vec;
367       ierr = CeedOperatorFieldGetVector(opinputfields[i], &vec); CeedChk(ierr);
368       if (vec == CEED_VECTOR_ACTIVE)
369         continue;
370     }
371     // Restore input
372     ierr = CeedQFunctionFieldGetEvalMode(qfinputfields[i], &emode);
373     CeedChk(ierr);
374     if (emode == CEED_EVAL_WEIGHT) { // Skip
375     } else {
376       ierr = CeedVectorRestoreArrayRead(impl->evecs[i],
377                                         (const CeedScalar **) &impl->edata[i]);
378       CeedChk(ierr);
379     }
380   }
381   return 0;
382 }
383 
384 //------------------------------------------------------------------------------
385 // Operator Apply
386 //------------------------------------------------------------------------------
387 static int CeedOperatorApply_Ref(CeedOperator op, CeedVector invec,
388                                  CeedVector outvec, CeedRequest *request) {
389   int ierr;
390   CeedOperator_Ref *impl;
391   ierr = CeedOperatorGetData(op, (void *)&impl); CeedChk(ierr);
392   CeedQFunction qf;
393   ierr = CeedOperatorGetQFunction(op, &qf); CeedChk(ierr);
394   CeedInt Q, numelements, numinputfields, numoutputfields, size;
395   ierr = CeedOperatorGetNumQuadraturePoints(op, &Q); CeedChk(ierr);
396   ierr = CeedOperatorGetNumElements(op, &numelements); CeedChk(ierr);
397   ierr= CeedQFunctionGetNumArgs(qf, &numinputfields, &numoutputfields);
398   CeedChk(ierr);
399   CeedOperatorField *opinputfields, *opoutputfields;
400   ierr = CeedOperatorGetFields(op, &opinputfields, &opoutputfields);
401   CeedChk(ierr);
402   CeedQFunctionField *qfinputfields, *qfoutputfields;
403   ierr = CeedQFunctionGetFields(qf, &qfinputfields, &qfoutputfields);
404   CeedChk(ierr);
405   CeedEvalMode emode;
406   CeedVector vec;
407   CeedElemRestriction Erestrict;
408 
409   // Setup
410   ierr = CeedOperatorSetup_Ref(op); CeedChk(ierr);
411 
412   // Input Evecs and Restriction
413   ierr = CeedOperatorSetupInputs_Ref(numinputfields, qfinputfields,
414                                      opinputfields, invec, false, impl,
415                                      request); CeedChk(ierr);
416 
417   // Output Evecs
418   for (CeedInt i=0; i<numoutputfields; i++) {
419     ierr = CeedVectorGetArray(impl->evecs[i+impl->numein], CEED_MEM_HOST,
420                               &impl->edata[i + numinputfields]); CeedChk(ierr);
421   }
422 
423   // Loop through elements
424   for (CeedInt e=0; e<numelements; e++) {
425     // Output pointers
426     for (CeedInt i=0; i<numoutputfields; i++) {
427       ierr = CeedQFunctionFieldGetEvalMode(qfoutputfields[i], &emode);
428       CeedChk(ierr);
429       if (emode == CEED_EVAL_NONE) {
430         ierr = CeedQFunctionFieldGetSize(qfoutputfields[i], &size);
431         CeedChk(ierr);
432         ierr = CeedVectorSetArray(impl->qvecsout[i], CEED_MEM_HOST,
433                                   CEED_USE_POINTER,
434                                   &impl->edata[i + numinputfields][e*Q*size]);
435         CeedChk(ierr);
436       }
437     }
438 
439     // Input basis apply
440     ierr = CeedOperatorInputBasis_Ref(e, Q, qfinputfields, opinputfields,
441                                       numinputfields, false, impl);
442     CeedChk(ierr);
443 
444     // Q function
445     if (!impl->identityqf) {
446       ierr = CeedQFunctionApply(qf, Q, impl->qvecsin, impl->qvecsout);
447       CeedChk(ierr);
448     }
449 
450     // Output basis apply
451     ierr = CeedOperatorOutputBasis_Ref(e, Q, qfoutputfields, opoutputfields,
452                                        numinputfields, numoutputfields, op, impl);
453     CeedChk(ierr);
454   }
455 
456   // Output restriction
457   for (CeedInt i=0; i<numoutputfields; i++) {
458     // Restore evec
459     ierr = CeedVectorRestoreArray(impl->evecs[i+impl->numein],
460                                   &impl->edata[i + numinputfields]);
461     CeedChk(ierr);
462     // Get output vector
463     ierr = CeedOperatorFieldGetVector(opoutputfields[i], &vec); CeedChk(ierr);
464     // Active
465     if (vec == CEED_VECTOR_ACTIVE)
466       vec = outvec;
467     // Restrict
468     ierr = CeedOperatorFieldGetElemRestriction(opoutputfields[i], &Erestrict);
469     CeedChk(ierr);
470     ierr = CeedElemRestrictionApply(Erestrict, CEED_TRANSPOSE,
471                                     impl->evecs[i+impl->numein], vec, request);
472     CeedChk(ierr);
473   }
474 
475   // Restore input arrays
476   ierr = CeedOperatorRestoreInputs_Ref(numinputfields, qfinputfields,
477                                        opinputfields, false, impl);
478   CeedChk(ierr);
479 
480   return 0;
481 }
482 
483 //------------------------------------------------------------------------------
484 // Assemble Linear QFunction
485 //------------------------------------------------------------------------------
486 static int CeedOperatorAssembleLinearQFunction_Ref(CeedOperator op,
487     CeedVector *assembled, CeedElemRestriction *rstr, CeedRequest *request) {
488   int ierr;
489   CeedOperator_Ref *impl;
490   ierr = CeedOperatorGetData(op, (void *)&impl); CeedChk(ierr);
491   CeedQFunction qf;
492   ierr = CeedOperatorGetQFunction(op, &qf); CeedChk(ierr);
493   CeedInt Q, numelements, numinputfields, numoutputfields, size;
494   ierr = CeedOperatorGetNumQuadraturePoints(op, &Q); CeedChk(ierr);
495   ierr = CeedOperatorGetNumElements(op, &numelements); CeedChk(ierr);
496   ierr= CeedQFunctionGetNumArgs(qf, &numinputfields, &numoutputfields);
497   CeedChk(ierr);
498   CeedOperatorField *opinputfields, *opoutputfields;
499   ierr = CeedOperatorGetFields(op, &opinputfields, &opoutputfields);
500   CeedChk(ierr);
501   CeedQFunctionField *qfinputfields, *qfoutputfields;
502   ierr = CeedQFunctionGetFields(qf, &qfinputfields, &qfoutputfields);
503   CeedChk(ierr);
504   CeedVector vec;
505   CeedInt numactivein = 0, numactiveout = 0;
506   CeedVector *activein = NULL;
507   CeedScalar *a, *tmp;
508   Ceed ceed, ceedparent;
509   ierr = CeedOperatorGetCeed(op, &ceed); CeedChk(ierr);
510   ierr = CeedGetOperatorFallbackParentCeed(ceed, &ceedparent); CeedChk(ierr);
511   ceedparent = ceedparent ? ceedparent : ceed;
512 
513   // Setup
514   ierr = CeedOperatorSetup_Ref(op); CeedChk(ierr);
515 
516   // Check for identity
517   if (impl->identityqf)
518     // LCOV_EXCL_START
519     return CeedError(ceed, 1, "Assembling identity qfunctions not supported");
520   // LCOV_EXCL_STOP
521 
522   // Input Evecs and Restriction
523   ierr = CeedOperatorSetupInputs_Ref(numinputfields, qfinputfields,
524                                      opinputfields, NULL, true, impl, request);
525   CeedChk(ierr);
526 
527   // Count number of active input fields
528   for (CeedInt i=0; i<numinputfields; i++) {
529     // Get input vector
530     ierr = CeedOperatorFieldGetVector(opinputfields[i], &vec); CeedChk(ierr);
531     // Check if active input
532     if (vec == CEED_VECTOR_ACTIVE) {
533       ierr = CeedQFunctionFieldGetSize(qfinputfields[i], &size); CeedChk(ierr);
534       ierr = CeedVectorSetValue(impl->qvecsin[i], 0.0); CeedChk(ierr);
535       ierr = CeedVectorGetArray(impl->qvecsin[i], CEED_MEM_HOST, &tmp);
536       CeedChk(ierr);
537       ierr = CeedRealloc(numactivein + size, &activein); CeedChk(ierr);
538       for (CeedInt field=0; field<size; field++) {
539         ierr = CeedVectorCreate(ceed, Q, &activein[numactivein+field]);
540         CeedChk(ierr);
541         ierr = CeedVectorSetArray(activein[numactivein+field], CEED_MEM_HOST,
542                                   CEED_USE_POINTER, &tmp[field*Q]);
543         CeedChk(ierr);
544       }
545       numactivein += size;
546       ierr = CeedVectorRestoreArray(impl->qvecsin[i], &tmp); CeedChk(ierr);
547     }
548   }
549 
550   // Count number of active output fields
551   for (CeedInt i=0; i<numoutputfields; i++) {
552     // Get output vector
553     ierr = CeedOperatorFieldGetVector(opoutputfields[i], &vec); CeedChk(ierr);
554     // Check if active output
555     if (vec == CEED_VECTOR_ACTIVE) {
556       ierr = CeedQFunctionFieldGetSize(qfoutputfields[i], &size); CeedChk(ierr);
557       numactiveout += size;
558     }
559   }
560 
561   // Check sizes
562   if (!numactivein || !numactiveout)
563     // LCOV_EXCL_START
564     return CeedError(ceed, 1, "Cannot assemble QFunction without active inputs "
565                      "and outputs");
566   // LCOV_EXCL_STOP
567 
568   // Create output restriction
569   CeedInt strides[3] = {1, Q, numactivein *numactiveout*Q};
570   ierr = CeedElemRestrictionCreateStrided(ceedparent, numelements, Q,
571                                           numelements*Q,
572                                           numactivein*numactiveout, strides,
573                                           rstr); CeedChk(ierr);
574   // Create assembled vector
575   ierr = CeedVectorCreate(ceedparent, numelements*Q*numactivein*numactiveout,
576                           assembled); CeedChk(ierr);
577   ierr = CeedVectorSetValue(*assembled, 0.0); CeedChk(ierr);
578   ierr = CeedVectorGetArray(*assembled, CEED_MEM_HOST, &a); CeedChk(ierr);
579 
580   // Loop through elements
581   for (CeedInt e=0; e<numelements; e++) {
582     // Input basis apply
583     ierr = CeedOperatorInputBasis_Ref(e, Q, qfinputfields, opinputfields,
584                                       numinputfields, true, impl);
585     CeedChk(ierr);
586 
587     // Assemble QFunction
588     for (CeedInt in=0; in<numactivein; in++) {
589       // Set Inputs
590       ierr = CeedVectorSetValue(activein[in], 1.0); CeedChk(ierr);
591       if (numactivein > 1) {
592         ierr = CeedVectorSetValue(activein[(in+numactivein-1)%numactivein],
593                                   0.0); CeedChk(ierr);
594       }
595       // Set Outputs
596       for (CeedInt out=0; out<numoutputfields; out++) {
597         // Get output vector
598         ierr = CeedOperatorFieldGetVector(opoutputfields[out], &vec);
599         CeedChk(ierr);
600         // Check if active output
601         if (vec == CEED_VECTOR_ACTIVE) {
602           CeedVectorSetArray(impl->qvecsout[out], CEED_MEM_HOST,
603                              CEED_USE_POINTER, a); CeedChk(ierr);
604           ierr = CeedQFunctionFieldGetSize(qfoutputfields[out], &size);
605           CeedChk(ierr);
606           a += size*Q; // Advance the pointer by the size of the output
607         }
608       }
609       // Apply QFunction
610       ierr = CeedQFunctionApply(qf, Q, impl->qvecsin, impl->qvecsout);
611       CeedChk(ierr);
612     }
613   }
614 
615   // Un-set output Qvecs to prevent accidental overwrite of Assembled
616   for (CeedInt out=0; out<numoutputfields; out++) {
617     // Get output vector
618     ierr = CeedOperatorFieldGetVector(opoutputfields[out], &vec);
619     CeedChk(ierr);
620     // Check if active output
621     if (vec == CEED_VECTOR_ACTIVE) {
622       CeedVectorSetArray(impl->qvecsout[out], CEED_MEM_HOST, CEED_COPY_VALUES,
623                          NULL); CeedChk(ierr);
624     }
625   }
626 
627   // Restore input arrays
628   ierr = CeedOperatorRestoreInputs_Ref(numinputfields, qfinputfields,
629                                        opinputfields, true, impl);
630   CeedChk(ierr);
631 
632   // Restore output
633   ierr = CeedVectorRestoreArray(*assembled, &a); CeedChk(ierr);
634 
635   // Cleanup
636   for (CeedInt i=0; i<numactivein; i++) {
637     ierr = CeedVectorDestroy(&activein[i]); CeedChk(ierr);
638   }
639   ierr = CeedFree(&activein); CeedChk(ierr);
640 
641   return 0;
642 }
643 
644 //------------------------------------------------------------------------------
645 // Get Basis Emode Pointer
646 //------------------------------------------------------------------------------
647 static inline void CeedOperatorGetBasisPointer_Ref(CeedScalar **basisptr,
648     CeedEvalMode emode, CeedScalar *identity, CeedScalar *interp,
649     CeedScalar *grad) {
650   switch (emode) {
651   case CEED_EVAL_NONE:
652     *basisptr = identity;
653     break;
654   case CEED_EVAL_INTERP:
655     *basisptr = interp;
656     break;
657   case CEED_EVAL_GRAD:
658     *basisptr = grad;
659     break;
660   case CEED_EVAL_WEIGHT:
661   case CEED_EVAL_DIV:
662   case CEED_EVAL_CURL:
663     break; // Caught by QF Assembly
664   }
665 }
666 
667 //------------------------------------------------------------------------------
668 // Assemble Linear Diagonal
669 //------------------------------------------------------------------------------
670 static int CeedOperatorAssembleLinearDiagonal_Ref(CeedOperator op,
671     CeedVector *assembled, CeedRequest *request) {
672   int ierr;
673 
674   // Assemble QFunction
675   CeedQFunction qf;
676   ierr = CeedOperatorGetQFunction(op, &qf); CeedChk(ierr);
677   CeedInt numinputfields, numoutputfields;
678   ierr= CeedQFunctionGetNumArgs(qf, &numinputfields, &numoutputfields);
679   CeedChk(ierr);
680   CeedVector assembledqf;
681   CeedElemRestriction rstr;
682   ierr = CeedOperatorAssembleLinearQFunction(op,  &assembledqf, &rstr, request);
683   CeedChk(ierr);
684   ierr = CeedElemRestrictionDestroy(&rstr); CeedChk(ierr);
685   CeedScalar maxnorm = 0;
686   ierr = CeedVectorNorm(assembledqf, CEED_NORM_MAX, &maxnorm); CeedChk(ierr);
687 
688   // Determine active input basis
689   CeedOperatorField *opfields;
690   CeedQFunctionField *qffields;
691   ierr = CeedOperatorGetFields(op, &opfields, NULL); CeedChk(ierr);
692   ierr = CeedQFunctionGetFields(qf, &qffields, NULL); CeedChk(ierr);
693   CeedInt numemodein = 0, ncomp, dim = 1;
694   CeedEvalMode *emodein = NULL;
695   CeedBasis basisin = NULL;
696   CeedElemRestriction rstrin = NULL;
697   for (CeedInt i=0; i<numinputfields; i++) {
698     CeedVector vec;
699     ierr = CeedOperatorFieldGetVector(opfields[i], &vec); CeedChk(ierr);
700     if (vec == CEED_VECTOR_ACTIVE) {
701       ierr = CeedOperatorFieldGetBasis(opfields[i], &basisin); CeedChk(ierr);
702       ierr = CeedBasisGetNumComponents(basisin, &ncomp); CeedChk(ierr);
703       ierr = CeedBasisGetDimension(basisin, &dim); CeedChk(ierr);
704       ierr = CeedOperatorFieldGetElemRestriction(opfields[i], &rstrin);
705       CeedChk(ierr);
706       CeedEvalMode emode;
707       ierr = CeedQFunctionFieldGetEvalMode(qffields[i], &emode);
708       CeedChk(ierr);
709       switch (emode) {
710       case CEED_EVAL_NONE:
711       case CEED_EVAL_INTERP:
712         ierr = CeedRealloc(numemodein + 1, &emodein); CeedChk(ierr);
713         emodein[numemodein] = emode;
714         numemodein += 1;
715         break;
716       case CEED_EVAL_GRAD:
717         ierr = CeedRealloc(numemodein + dim, &emodein); CeedChk(ierr);
718         for (CeedInt d=0; d<dim; d++)
719           emodein[numemodein+d] = emode;
720         numemodein += dim;
721         break;
722       case CEED_EVAL_WEIGHT:
723       case CEED_EVAL_DIV:
724       case CEED_EVAL_CURL:
725         break; // Caught by QF Assembly
726       }
727     }
728   }
729 
730   // Determine active output basis
731   ierr = CeedOperatorGetFields(op, NULL, &opfields); CeedChk(ierr);
732   ierr = CeedQFunctionGetFields(qf, NULL, &qffields); CeedChk(ierr);
733   CeedInt numemodeout = 0;
734   CeedEvalMode *emodeout = NULL;
735   CeedBasis basisout = NULL;
736   CeedElemRestriction rstrout = NULL;
737   for (CeedInt i=0; i<numoutputfields; i++) {
738     CeedVector vec;
739     ierr = CeedOperatorFieldGetVector(opfields[i], &vec); CeedChk(ierr);
740     if (vec == CEED_VECTOR_ACTIVE) {
741       ierr = CeedOperatorFieldGetBasis(opfields[i], &basisout); CeedChk(ierr);
742       ierr = CeedOperatorFieldGetElemRestriction(opfields[i], &rstrout);
743       CeedChk(ierr);
744       CeedEvalMode emode;
745       ierr = CeedQFunctionFieldGetEvalMode(qffields[i], &emode); CeedChk(ierr);
746       switch (emode) {
747       case CEED_EVAL_NONE:
748       case CEED_EVAL_INTERP:
749         ierr = CeedRealloc(numemodeout + 1, &emodeout); CeedChk(ierr);
750         emodeout[numemodeout] = emode;
751         numemodeout += 1;
752         break;
753       case CEED_EVAL_GRAD:
754         ierr = CeedRealloc(numemodeout + dim, &emodeout); CeedChk(ierr);
755         for (CeedInt d=0; d<dim; d++)
756           emodeout[numemodeout+d] = emode;
757         numemodeout += dim;
758         break;
759       case CEED_EVAL_WEIGHT:
760       case CEED_EVAL_DIV:
761       case CEED_EVAL_CURL:
762         break; // Caught by QF Assembly
763       }
764     }
765   }
766 
767   // Create diagonal vector
768   CeedVector elemdiag;
769   ierr = CeedElemRestrictionCreateVector(rstrin, assembled, &elemdiag);
770   CeedChk(ierr);
771 
772   // Assemble element operator diagonals
773   CeedScalar *elemdiagarray, *assembledqfarray;
774   ierr = CeedVectorSetValue(elemdiag, 0.0); CeedChk(ierr);
775   ierr = CeedVectorGetArray(elemdiag, CEED_MEM_HOST, &elemdiagarray);
776   CeedChk(ierr);
777   ierr = CeedVectorGetArray(assembledqf, CEED_MEM_HOST, &assembledqfarray);
778   CeedChk(ierr);
779   CeedInt nelem, nnodes, nqpts;
780   ierr = CeedElemRestrictionGetNumElements(rstrin, &nelem); CeedChk(ierr);
781   ierr = CeedBasisGetNumNodes(basisin, &nnodes); CeedChk(ierr);
782   ierr = CeedBasisGetNumQuadraturePoints(basisin, &nqpts); CeedChk(ierr);
783   // Basis matrices
784   CeedScalar *identity = NULL, *interpin, *interpout, *gradin, *gradout;
785   bool evalNone = false;
786   for (CeedInt i=0; i<numemodein; i++)
787     evalNone = evalNone || (emodein[i] == CEED_EVAL_NONE);
788   for (CeedInt i=0; i<numemodeout; i++)
789     evalNone = evalNone || (emodeout[i] == CEED_EVAL_NONE);
790   if (evalNone) {
791     ierr = CeedCalloc(nqpts*nnodes, &identity); CeedChk(ierr);
792     for (CeedInt i=0; i<(nnodes<nqpts?nnodes:nqpts); i++)
793       identity[i*nnodes+i] = 1.0;
794   }
795   ierr = CeedBasisGetInterp(basisin, &interpin); CeedChk(ierr);
796   ierr = CeedBasisGetInterp(basisout, &interpout); CeedChk(ierr);
797   ierr = CeedBasisGetGrad(basisin, &gradin); CeedChk(ierr);
798   ierr = CeedBasisGetGrad(basisout, &gradout); CeedChk(ierr);
799   // Compute the diagonal of B^T D B
800   // Each element
801   for (CeedInt e=0; e<nelem; e++) {
802     CeedInt dout = -1;
803     // Each basis eval mode pair
804     for (CeedInt eout=0; eout<numemodeout; eout++) {
805       CeedScalar *bt = NULL;
806       if (emodeout[eout] == CEED_EVAL_GRAD)
807         dout += 1;
808       CeedOperatorGetBasisPointer_Ref(&bt, emodeout[eout], identity, interpout,
809                                       &gradout[dout*nqpts*nnodes]);
810       CeedInt din = -1;
811       for (CeedInt ein=0; ein<numemodein; ein++) {
812         CeedScalar *b = NULL;
813         if (emodein[ein] == CEED_EVAL_GRAD)
814           din += 1;
815         CeedOperatorGetBasisPointer_Ref(&b, emodein[ein], identity, interpin,
816                                         &gradin[din*nqpts*nnodes]);
817         // Each component
818         for (CeedInt comp=0; comp<ncomp; comp++)
819           // Each qpoint/node pair
820           for (CeedInt q=0; q<nqpts; q++) {
821             const CeedScalar qfvalue =
822               assembledqfarray[((((e*numemodein+ein)*ncomp+comp)*
823                                  numemodeout+eout)*ncomp+comp)*nqpts+q];
824             if (fabs(qfvalue) > maxnorm*1e-12)
825               for (CeedInt n=0; n<nnodes; n++)
826                 elemdiagarray[(e*ncomp+comp)*nnodes+n] += bt[q*nnodes+n] *
827                     qfvalue * b[q*nnodes+n];
828           }
829       }
830     }
831   }
832   ierr = CeedVectorRestoreArray(elemdiag, &elemdiagarray); CeedChk(ierr);
833   ierr = CeedVectorRestoreArray(assembledqf, &assembledqfarray); CeedChk(ierr);
834 
835   // Assemble local operator diagonal
836   ierr = CeedVectorSetValue(*assembled, 0.0); CeedChk(ierr);
837   ierr = CeedElemRestrictionApply(rstrout, CEED_TRANSPOSE, elemdiag,
838                                   *assembled, request); CeedChk(ierr);
839 
840   // Cleanup
841   ierr = CeedVectorDestroy(&assembledqf); CeedChk(ierr);
842   ierr = CeedVectorDestroy(&elemdiag); CeedChk(ierr);
843   ierr = CeedFree(&emodein); CeedChk(ierr);
844   ierr = CeedFree(&emodeout); CeedChk(ierr);
845   ierr = CeedFree(&identity); CeedChk(ierr);
846 
847   return 0;
848 }
849 
850 //------------------------------------------------------------------------------
851 // Create FDM Element Inverse
852 //------------------------------------------------------------------------------
853 int CeedOperatorCreateFDMElementInverse_Ref(CeedOperator op,
854     CeedOperator *fdminv, CeedRequest *request) {
855   int ierr;
856   Ceed ceed, ceedparent;
857   ierr = CeedOperatorGetCeed(op, &ceed); CeedChk(ierr);
858   ierr = CeedGetOperatorFallbackParentCeed(ceed, &ceedparent); CeedChk(ierr);
859   ceedparent = ceedparent ? ceedparent : ceed;
860   CeedQFunction qf;
861   ierr = CeedOperatorGetQFunction(op, &qf); CeedChk(ierr);
862 
863   // Determine active input basis
864   bool interp = false, grad = false;
865   CeedBasis basis = NULL;
866   CeedElemRestriction rstr = NULL;
867   CeedOperatorField *opfields;
868   CeedQFunctionField *qffields;
869   ierr = CeedOperatorGetFields(op, &opfields, NULL); CeedChk(ierr);
870   ierr = CeedQFunctionGetFields(qf, &qffields, NULL); CeedChk(ierr);
871   CeedInt numinputfields;
872   ierr = CeedQFunctionGetNumArgs(qf, &numinputfields, NULL); CeedChk(ierr);
873   for (CeedInt i=0; i<numinputfields; i++) {
874     CeedVector vec;
875     ierr = CeedOperatorFieldGetVector(opfields[i], &vec); CeedChk(ierr);
876     if (vec == CEED_VECTOR_ACTIVE) {
877       CeedEvalMode emode;
878       ierr = CeedQFunctionFieldGetEvalMode(qffields[i], &emode); CeedChk(ierr);
879       interp = interp || emode == CEED_EVAL_INTERP;
880       grad = grad || emode == CEED_EVAL_GRAD;
881       ierr = CeedOperatorFieldGetBasis(opfields[i], &basis); CeedChk(ierr);
882       ierr = CeedOperatorFieldGetElemRestriction(opfields[i], &rstr);
883       CeedChk(ierr);
884     }
885   }
886   if (!basis)
887     // LCOV_EXCL_START
888     return CeedError(ceed, 1, "No active field set");
889   // LCOV_EXCL_STOP
890   CeedInt P1d, Q1d, elemsize, nqpts, dim, ncomp = 1, nelem = 1, nnodes = 1;
891   ierr = CeedBasisGetNumNodes1D(basis, &P1d); CeedChk(ierr);
892   ierr = CeedBasisGetNumNodes(basis, &elemsize); CeedChk(ierr);
893   ierr = CeedBasisGetNumQuadraturePoints1D(basis, &Q1d); CeedChk(ierr);
894   ierr = CeedBasisGetNumQuadraturePoints(basis, &nqpts); CeedChk(ierr);
895   ierr = CeedBasisGetDimension(basis, &dim); CeedChk(ierr);
896   ierr = CeedBasisGetNumComponents(basis, &ncomp); CeedChk(ierr);
897   ierr = CeedElemRestrictionGetNumElements(rstr, &nelem); CeedChk(ierr);
898   ierr = CeedElemRestrictionGetNumNodes(rstr, &nnodes); CeedChk(ierr);
899 
900   // Build and diagonalize 1D Mass and Laplacian
901   bool tensorbasis;
902   ierr = CeedBasisGetTensorStatus(basis, &tensorbasis); CeedChk(ierr);
903   if (!tensorbasis)
904     // LCOV_EXCL_START
905     return CeedError(ceed, 1, "FDMElementInverse only supported for tensor "
906                      "bases");
907   // LCOV_EXCL_STOP
908   CeedScalar *work, *mass, *laplace, *x, *x2, *lambda;
909   ierr = CeedMalloc(Q1d*P1d, &work); CeedChk(ierr);
910   ierr = CeedMalloc(P1d*P1d, &mass); CeedChk(ierr);
911   ierr = CeedMalloc(P1d*P1d, &laplace); CeedChk(ierr);
912   ierr = CeedMalloc(P1d*P1d, &x); CeedChk(ierr);
913   ierr = CeedMalloc(P1d*P1d, &x2); CeedChk(ierr);
914   ierr = CeedMalloc(P1d, &lambda); CeedChk(ierr);
915   // -- Mass
916   CeedScalar *interp1d, *grad1d, *qweight1d;
917   ierr = CeedBasisGetInterp1D(basis, &interp1d); CeedChk(ierr);
918   ierr = CeedBasisGetGrad1D(basis, &grad1d); CeedChk(ierr);
919   ierr = CeedBasisGetQWeights(basis, &qweight1d); CeedChk(ierr);
920   for (CeedInt i=0; i<Q1d; i++)
921     for (CeedInt j=0; j<P1d; j++)
922       work[i+j*Q1d] = interp1d[i*P1d+j]*qweight1d[i];
923   ierr = CeedMatrixMultiply(ceed, (const CeedScalar *)work,
924                             (const CeedScalar *)interp1d, mass, P1d, P1d, Q1d);
925   CeedChk(ierr);
926   // -- Laplacian
927   for (CeedInt i=0; i<Q1d; i++)
928     for (CeedInt j=0; j<P1d; j++)
929       work[i+j*Q1d] = grad1d[i*P1d+j]*qweight1d[i];
930   ierr = CeedMatrixMultiply(ceed, (const CeedScalar *)work,
931                             (const CeedScalar *)grad1d, laplace, P1d, P1d, Q1d);
932   CeedChk(ierr);
933   // -- Diagonalize
934   ierr = CeedSimultaneousDiagonalization(ceed, laplace, mass, x, lambda, P1d);
935   CeedChk(ierr);
936   ierr = CeedFree(&work); CeedChk(ierr);
937   ierr = CeedFree(&mass); CeedChk(ierr);
938   ierr = CeedFree(&laplace); CeedChk(ierr);
939   for (CeedInt i=0; i<P1d; i++)
940     for (CeedInt j=0; j<P1d; j++)
941       x2[i+j*P1d] = x[j+i*P1d];
942   ierr = CeedFree(&x); CeedChk(ierr);
943 
944   // Assemble QFunction
945   CeedVector assembled;
946   CeedElemRestriction rstr_qf;
947   ierr =  CeedOperatorAssembleLinearQFunction(op, &assembled, &rstr_qf,
948           request); CeedChk(ierr);
949   ierr = CeedElemRestrictionDestroy(&rstr_qf); CeedChk(ierr);
950   CeedScalar maxnorm = 0;
951   ierr = CeedVectorNorm(assembled, CEED_NORM_MAX, &maxnorm); CeedChk(ierr);
952 
953   // Calculate element averages
954   CeedInt nfields = ((interp?1:0) + (grad?dim:0))*((interp?1:0) + (grad?dim:0));
955   CeedScalar *elemavg;
956   const CeedScalar *assembledarray, *qweightsarray;
957   CeedVector qweights;
958   ierr = CeedVectorCreate(ceedparent, nqpts, &qweights); CeedChk(ierr);
959   ierr = CeedBasisApply(basis, 1, CEED_NOTRANSPOSE, CEED_EVAL_WEIGHT,
960                         CEED_VECTOR_NONE, qweights); CeedChk(ierr);
961   ierr = CeedVectorGetArrayRead(assembled, CEED_MEM_HOST, &assembledarray);
962   CeedChk(ierr);
963   ierr = CeedVectorGetArrayRead(qweights, CEED_MEM_HOST, &qweightsarray);
964   CeedChk(ierr);
965   ierr = CeedCalloc(nelem, &elemavg); CeedChk(ierr);
966   for (CeedInt e=0; e<nelem; e++) {
967     CeedInt count = 0;
968     for (CeedInt q=0; q<nqpts; q++)
969       for (CeedInt i=0; i<ncomp*ncomp*nfields; i++)
970         if (fabs(assembledarray[e*nelem*nqpts*ncomp*ncomp*nfields +
971                                                                   i*nqpts + q]) > maxnorm*1e-12) {
972           elemavg[e] += assembledarray[e*nelem*nqpts*ncomp*ncomp*nfields +
973                                        i*nqpts + q] / qweightsarray[q];
974           count++;
975         }
976     if (count)
977       elemavg[e] /= count;
978   }
979   ierr = CeedVectorRestoreArrayRead(assembled, &assembledarray); CeedChk(ierr);
980   ierr = CeedVectorDestroy(&assembled); CeedChk(ierr);
981   ierr = CeedVectorRestoreArrayRead(qweights, &qweightsarray); CeedChk(ierr);
982   ierr = CeedVectorDestroy(&qweights); CeedChk(ierr);
983 
984   // Build FDM diagonal
985   CeedVector qdata;
986   CeedScalar *qdataarray;
987   ierr = CeedVectorCreate(ceedparent, nelem*ncomp*nnodes, &qdata); CeedChk(ierr);
988   ierr = CeedVectorSetArray(qdata, CEED_MEM_HOST, CEED_COPY_VALUES, NULL);
989   CeedChk(ierr);
990   ierr = CeedVectorGetArray(qdata, CEED_MEM_HOST, &qdataarray); CeedChk(ierr);
991   for (CeedInt e=0; e<nelem; e++)
992     for (CeedInt c=0; c<ncomp; c++)
993       for (CeedInt n=0; n<nnodes; n++) {
994         if (interp)
995           qdataarray[(e*ncomp+c)*nnodes+n] = 1;
996         if (grad)
997           for (CeedInt d=0; d<dim; d++) {
998             CeedInt i = (n / CeedIntPow(P1d, d)) % P1d;
999             qdataarray[(e*ncomp+c)*nnodes+n] += lambda[i];
1000           }
1001         qdataarray[(e*ncomp+c)*nnodes+n] = 1 / (elemavg[e] *
1002                                                 qdataarray[(e*ncomp+c)*nnodes+n]);
1003       }
1004   ierr = CeedFree(&elemavg); CeedChk(ierr);
1005   ierr = CeedVectorRestoreArray(qdata, &qdataarray); CeedChk(ierr);
1006 
1007   // Setup FDM operator
1008   // -- Basis
1009   CeedBasis fdm_basis;
1010   CeedScalar *graddummy, *qrefdummy, *qweightdummy;
1011   ierr = CeedCalloc(P1d*P1d, &graddummy); CeedChk(ierr);
1012   ierr = CeedCalloc(P1d, &qrefdummy); CeedChk(ierr);
1013   ierr = CeedCalloc(P1d, &qweightdummy); CeedChk(ierr);
1014   ierr = CeedBasisCreateTensorH1(ceedparent, dim, ncomp, P1d, P1d, x2,
1015                                  graddummy, qrefdummy, qweightdummy,
1016                                  &fdm_basis); CeedChk(ierr);
1017   ierr = CeedFree(&graddummy); CeedChk(ierr);
1018   ierr = CeedFree(&qrefdummy); CeedChk(ierr);
1019   ierr = CeedFree(&qweightdummy); CeedChk(ierr);
1020   ierr = CeedFree(&x2); CeedChk(ierr);
1021   ierr = CeedFree(&lambda); CeedChk(ierr);
1022 
1023   // -- Restriction
1024   CeedElemRestriction rstr_i;
1025   CeedInt strides[3] = {1, nnodes, nnodes*ncomp};
1026   ierr = CeedElemRestrictionCreateStrided(ceedparent, nelem, nnodes,
1027                                           nnodes*nelem, ncomp, strides, &rstr_i);
1028   CeedChk(ierr);
1029   // -- QFunction
1030   CeedQFunction mass_qf;
1031   ierr = CeedQFunctionCreateInteriorByName(ceedparent, "MassApply", &mass_qf);
1032   CeedChk(ierr);
1033   // -- Operator
1034   ierr = CeedOperatorCreate(ceedparent, mass_qf, NULL, NULL, fdminv);
1035   CeedChk(ierr);
1036   CeedOperatorSetField(*fdminv, "u", rstr_i, fdm_basis, CEED_VECTOR_ACTIVE);
1037   CeedChk(ierr);
1038   CeedOperatorSetField(*fdminv, "qdata", rstr_i, CEED_BASIS_COLLOCATED, qdata);
1039   CeedChk(ierr);
1040   CeedOperatorSetField(*fdminv, "v", rstr_i, fdm_basis, CEED_VECTOR_ACTIVE);
1041   CeedChk(ierr);
1042 
1043   // Cleanup
1044   ierr = CeedVectorDestroy(&qdata); CeedChk(ierr);
1045   ierr = CeedBasisDestroy(&fdm_basis); CeedChk(ierr);
1046   ierr = CeedElemRestrictionDestroy(&rstr_i); CeedChk(ierr);
1047   ierr = CeedQFunctionDestroy(&mass_qf); CeedChk(ierr);
1048 
1049   return 0;
1050 }
1051 
1052 //------------------------------------------------------------------------------
1053 // Operator Destroy
1054 //------------------------------------------------------------------------------
1055 static int CeedOperatorDestroy_Ref(CeedOperator op) {
1056   int ierr;
1057   CeedOperator_Ref *impl;
1058   ierr = CeedOperatorGetData(op, (void *)&impl); CeedChk(ierr);
1059 
1060   for (CeedInt i=0; i<impl->numein+impl->numeout; i++) {
1061     ierr = CeedVectorDestroy(&impl->evecs[i]); CeedChk(ierr);
1062   }
1063   ierr = CeedFree(&impl->evecs); CeedChk(ierr);
1064   ierr = CeedFree(&impl->edata); CeedChk(ierr);
1065   ierr = CeedFree(&impl->inputstate); CeedChk(ierr);
1066 
1067   for (CeedInt i=0; i<impl->numein; i++) {
1068     ierr = CeedVectorDestroy(&impl->evecsin[i]); CeedChk(ierr);
1069     ierr = CeedVectorDestroy(&impl->qvecsin[i]); CeedChk(ierr);
1070   }
1071   ierr = CeedFree(&impl->evecsin); CeedChk(ierr);
1072   ierr = CeedFree(&impl->qvecsin); CeedChk(ierr);
1073 
1074   for (CeedInt i=0; i<impl->numeout; i++) {
1075     ierr = CeedVectorDestroy(&impl->evecsout[i]); CeedChk(ierr);
1076     ierr = CeedVectorDestroy(&impl->qvecsout[i]); CeedChk(ierr);
1077   }
1078   ierr = CeedFree(&impl->evecsout); CeedChk(ierr);
1079   ierr = CeedFree(&impl->qvecsout); CeedChk(ierr);
1080 
1081   ierr = CeedFree(&impl); CeedChk(ierr);
1082   return 0;
1083 }
1084 
1085 //------------------------------------------------------------------------------
1086 // Operator Create
1087 //------------------------------------------------------------------------------
1088 int CeedOperatorCreate_Ref(CeedOperator op) {
1089   int ierr;
1090   Ceed ceed;
1091   ierr = CeedOperatorGetCeed(op, &ceed); CeedChk(ierr);
1092   CeedOperator_Ref *impl;
1093 
1094   ierr = CeedCalloc(1, &impl); CeedChk(ierr);
1095   ierr = CeedOperatorSetData(op, (void *)&impl); CeedChk(ierr);
1096 
1097   ierr = CeedSetBackendFunction(ceed, "Operator", op, "AssembleLinearQFunction",
1098                                 CeedOperatorAssembleLinearQFunction_Ref);
1099   CeedChk(ierr);
1100   ierr = CeedSetBackendFunction(ceed, "Operator", op, "AssembleLinearDiagonal",
1101                                 CeedOperatorAssembleLinearDiagonal_Ref);
1102   CeedChk(ierr);
1103   ierr = CeedSetBackendFunction(ceed, "Operator", op, "CreateFDMElementInverse",
1104                                 CeedOperatorCreateFDMElementInverse_Ref);
1105   CeedChk(ierr);
1106   ierr = CeedSetBackendFunction(ceed, "Operator", op, "ApplyAdd",
1107                                 CeedOperatorApply_Ref); CeedChk(ierr);
1108   ierr = CeedSetBackendFunction(ceed, "Operator", op, "Destroy",
1109                                 CeedOperatorDestroy_Ref); CeedChk(ierr);
1110   return 0;
1111 }
1112 //------------------------------------------------------------------------------
1113